Question

С 3 НОМЕРОМ РЕБЯТ ПОМОГИТЕ ПОЖАЛУЙСТА!

Answer 1

cos(70)*cos(10)+cos(80)*cos(20)=sin(20)*cos(10)+sin(10)*cos(20)=sin(10+20)=sin(30)
cos(69)*cos(9)+cos(81)*cos(21)=sin(21)*cos(9)+sin(9)*cos(21)=sin(21+9)=sin(30)

{cos(70)*cos(10)+cos(80)*cos(20)} : {cos(69)*cos(9)+cos(81)*cos(21)} = sin(30)/sin(30) = 1

Answer 2

3
(сos70cos10+cos80cos20)/(cos69cos9+cos81cos21)=
=(сos70cos10+cos(90-10)cos(90-70))/(cos69cos9+cos(90-9)cos(90-69))=
=(сos70cos10+sin10sin70)/(cos69cos9+sin9sin69)=cos(70-10)/cos(69-9)=
=cos60/cos60=1
4
sin3π/10-sinπ/10=sin[(3π/10-π/10)/2]cos[(3π/10+π/10)/2]=2sinπ/10cosπ/5≠1/2
5
cos(x-3π/2)=-4/5
-sinx=-4/5
sinx=4/5
cosx=√(1-sin²x)=√(1-16/25)=3/5
sin(x/2)cos(5x/2)=1/2(sin(x/2-5x/2)+sin(x/2+5x/2))=1/2(-sin2x+sin3x)
sin2x=2sinxcosx=2*4/5*3/5=24/25
sin3x=3sinx-4sin³x=3*4/5-4*64/125=12/5-256/125=300/125-256/125=44/125
sin(x/2)cos(5x/2)==1/2(-24/25+44/125)=1/2*20/125=2/25=0,08